Details

analyze5.0ms

Algorithm

Search

True	Other	False	Iter
0%	56.2%	43.8%	0
0%	56.2%	43.8%	1
0%	56.2%	43.8%	2
42.1%	14%	43.8%	3
42.1%	14%	43.8%	4
52.7%	3.5%	43.8%	5
56.2%	0%	43.8%	6

sample27.0ms

Algorithm

intervals

Results

15.0ms	256×	body	80	valid
4.0ms	256×	pre	80	true

simplify533.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (514.0ms)

Iter	Nodes	Cost
0	5112	37

prune5.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 1.4b

Counts

2 → 2

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))
0.1b	(/.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
6.5b	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
10.5b	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

77×	`*-un-lft-identity_binary64`
34×	`distribute-lft-out_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
24×	`flip3-+_binary64` `flip-+_binary64`
21×	`associate-r_binary64` `add-sqr-sqrt_binary64`
18×	`associate-/r/_binary64`
16×	`frac-times_binary64`
15×	`add-cube-cbrt_binary64`
14×	`times-frac_binary64`
13×	`pow1_binary64`
11×	`swap-sqr_binary64`
10×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `prod-exp_binary64` `div-exp_binary64` `associate-*l/_binary64`
9×	`associate-l_binary64`
8×	`associate-*r/_binary64`
7×	`associate-/l/_binary64`
6×	`associate-/r*_binary64`
5×	`associate-/l*_binary64`
4×	`add-log-exp_binary64` `insert-posit16`
3×	`unswap-sqr_binary64` `div-inv_binary64`
2×	`pow-prod-down_binary64` `clear-num_binary64` `frac-2neg_binary64` `*-commutative_binary64`
1×	`pow-prod-up_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `pow-plus_binary64` `pow-sqr_binary64` `pow2_binary64`

Counts

4 → 162

Calls

4 calls:

21.0ms	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))
32.0ms	(/.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
28.0ms	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
20.0ms	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))

series1.5s

Counts

4 → 12

Calls

4 calls:

316.0ms	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))
454.0ms	(/.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
430.0ms	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
250.0ms	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	404	753
1	404	753
0	49	45
1	49	45
0	404	753
1	404	753
0	49	45
1	49	45
0	111	67
1	111	67
0	503	999
1	503	999
0	63	63
1	63	63
0	503	999
1	503	999
0	63	63
1	63	63
0	5101	12
0	676	1339
1	676	1339
0	105	517
1	105	517
0	676	1339
1	676	1339
0	105	517
1	105	517
0	5630	44
0	254	303
1	254	303
0	8	9
1	8	9
0	254	303
1	254	303
0	8	9
1	8	9
0	4997	21
1	4997	21

simplify62.0ms

Counts

174 → 174

Iterations

Useful iterations: 0 (10.0ms)

Iter	Nodes	Cost
0	647	5089
1	647	5089

prune218.0ms

Filtered

123 candidates to 174 candidates (-41.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	167	7	174
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	168	8	176

Merged error: 0.0b

Counts

176 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (+.f64 alpha beta) (*.f64 beta alpha))
0.0b	(/.f64 (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1) (+.f64 (+.f64 alpha beta) (.f64 2 1))) (+.f64 (+.f64 alpha beta) (*.f64 2 1)))
0.1b	(/.f64 (/.f64 (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1) (+.f64 (+.f64 alpha beta) (.f64 2 1))) (+.f64 (+.f64 alpha beta) (.f64 2 1))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 2 1)) 1))
3.1b	(/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1) (+.f64 (+.f64 alpha beta) (.f64 2 1)))

rewrite149.0ms

Algorithm

rewrite-expression-head

Rules

804×	`times-frac_binary64`
584×	`*-un-lft-identity_binary64`
340×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
122×	`distribute-lft-out_binary64`
82×	`associate-/l*_binary64`
54×	`associate-/r/_binary64`
29×	`flip3-+_binary64` `flip-+_binary64`
27×	`div-inv_binary64`
20×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`associate-/r*_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
9×	`add-log-exp_binary64`
4×	`associate-/l/_binary64` `pow1_binary64` `insert-posit16`
3×	`clear-num_binary64` `frac-2neg_binary64` `sum-log_binary64`
1×	`associate-+l+_binary64` `+-commutative_binary64`

Counts

4 → 467

Calls

4 calls:

8.0ms	(+.f64 (+.f64 alpha beta) (*.f64 beta alpha))
27.0ms	(/.f64 (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1) (+.f64 (+.f64 alpha beta) (.f64 2 1))) (+.f64 (+.f64 alpha beta) (*.f64 2 1)))
48.0ms	(/.f64 (/.f64 (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1) (+.f64 (+.f64 alpha beta) (.f64 2 1))) (+.f64 (+.f64 alpha beta) (.f64 2 1))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 2 1)) 1))
19.0ms	(/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1) (+.f64 (+.f64 alpha beta) (.f64 2 1)))

series1.4s

Counts

4 → 12

Calls

4 calls:

266.0ms	(+.f64 (+.f64 alpha beta) (*.f64 beta alpha))
448.0ms	(/.f64 (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1) (+.f64 (+.f64 alpha beta) (.f64 2 1))) (+.f64 (+.f64 alpha beta) (*.f64 2 1)))
352.0ms	(/.f64 (/.f64 (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1) (+.f64 (+.f64 alpha beta) (.f64 2 1))) (+.f64 (+.f64 alpha beta) (.f64 2 1))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 2 1)) 1))
314.0ms	(/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1) (+.f64 (+.f64 alpha beta) (.f64 2 1)))

Iterations

Useful iterations: 0 (92.0ms)

Iter	Nodes	Cost
0	466	591
1	466	591
0	10	9
1	10	9
0	466	591
1	466	591
0	10	9
1	10	9
0	17	36
1	17	36
0	751	1437
1	751	1437
0	78	531
1	78	531
0	751	1437
1	751	1437
0	78	531
1	78	531
0	30	12
1	30	12
0	584	1029
1	584	1029
0	34	51
1	34	51
0	584	1029
1	584	1029
0	34	51
1	34	51
0	17	18
1	17	18
0	263	195
1	263	195
0	12	21
1	12	21
0	263	195
1	263	195
0	12	21
1	12	21
0	10	3
1	10	3

simplify294.0ms

Counts

479 → 479

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	5206	28366

prune965.0ms

Filtered

291 candidates to 479 candidates (-64.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	475	4	479
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	479	8	487

Merged error: 0.0b

Counts

487 → 8

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(.f64 (sqrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 alpha beta)) 1)) (/.f64 (sqrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 alpha beta)) 1)) (+.f64 (+.f64 alpha beta) 2)))
0.2b	(/.f64 (sqrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 alpha beta)) 1)) (+.f64 (+.f64 alpha beta) 2))
3.1b	(sqrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 alpha beta)) 1))
3.1b	(sqrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 alpha beta)) 1))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

149×	`*-un-lft-identity_binary64`
74×	`times-frac_binary64`
64×	`add-sqr-sqrt_binary64`
61×	`sqrt-prod_binary64`
59×	`distribute-lft-out_binary64`
46×	`add-cube-cbrt_binary64`
41×	`associate-r_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`sqrt-div_binary64`
8×	`pow1_binary64`
7×	`flip3-+_binary64` `associate-l_binary64` `associate-/l*_binary64` `flip-+_binary64`
6×	`unswap-sqr_binary64`
5×	`associate-/r*_binary64`
4×	`add-log-exp_binary64` `associate-/r/_binary64` `insert-posit16`
2×	`associate-/l/_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `prod-exp_binary64` `div-inv_binary64` `div-exp_binary64` `frac-times_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `associate-r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `-commutative_binary64`

Counts

4 → 171

Calls

4 calls:

37.0ms	(.f64 (sqrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 alpha beta)) 1)) (/.f64 (sqrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 alpha beta)) 1)) (+.f64 (+.f64 alpha beta) 2)))
19.0ms	(/.f64 (sqrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 alpha beta)) 1)) (+.f64 (+.f64 alpha beta) 2))
9.0ms	(sqrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 alpha beta)) 1))
9.0ms	(sqrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 alpha beta)) 1))

series1.2s

Counts

4 → 12

Calls

4 calls:

322.0ms	(.f64 (sqrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 alpha beta)) 1)) (/.f64 (sqrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 alpha beta)) 1)) (+.f64 (+.f64 alpha beta) 2)))
276.0ms	(/.f64 (sqrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 alpha beta)) 1)) (+.f64 (+.f64 alpha beta) 2))
281.0ms	(sqrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 alpha beta)) 1))
281.0ms	(sqrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 alpha beta)) 1))

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	364	345
1	364	345
0	9	9
1	9	9
0	364	345
1	364	345
0	9	9
1	9	9
0	11	21
1	11	21
0	364	345
1	364	345
0	9	9
1	9	9
0	364	345
1	364	345
0	9	9
1	9	9
0	11	21
1	11	21
0	527	731
1	527	731
0	56	119
1	56	119
0	527	731
1	527	731
0	56	119
1	56	119
0	208	90
1	208	90
0	606	1323
1	606	1323
0	128	621
1	128	621
0	606	1323
1	606	1323
0	128	621
1	128	621
0	148	138
1	148	138

simplify72.0ms

Counts

183 → 183

Iterations

Useful iterations: 0 (10.0ms)

Iter	Nodes	Cost
0	416	6284
1	416	6284

prune246.0ms

Filtered

112 candidates to 183 candidates (-63.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	183	0	183
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	183	8	191

Merged error: 0.0b

Counts

191 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (+.f64 alpha beta) (*.f64 beta alpha))
0.0b	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 3))
2.6b	(/.f64 (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1) (+.f64 (+.f64 alpha beta) (.f64 2 1))) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 3)))
3.1b	(/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1) (+.f64 (+.f64 alpha beta) (.f64 2 1)))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

61×	`*-un-lft-identity_binary64`
54×	`times-frac_binary64`
33×	`add-sqr-sqrt_binary64`
31×	`add-cube-cbrt_binary64`
22×	`associate-/l*_binary64`
20×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
17×	`flip3-+_binary64` `flip-+_binary64`
16×	`distribute-lft-out_binary64`
14×	`associate-/r/_binary64`
9×	`add-log-exp_binary64`
8×	`frac-times_binary64`
7×	`cbrt-undiv_binary64` `div-exp_binary64`
6×	`pow1_binary64`
5×	`associate-r_binary64` `associate-l_binary64`
4×	`associate-/r_binary64` `associate-r/_binary64` `div-inv_binary64` `insert-posit16` `associate-*l/_binary64`
3×	`associate-/l/_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `sum-log_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64`
1×	`pow-prod-down_binary64` `associate-+l+_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `+-commutative_binary64` `*-commutative_binary64`

Counts

4 → 148

Calls

4 calls:

8.0ms	(+.f64 (+.f64 alpha beta) (*.f64 beta alpha))
18.0ms	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 3))
38.0ms	(/.f64 (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1) (+.f64 (+.f64 alpha beta) (.f64 2 1))) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 3)))
19.0ms	(/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1) (+.f64 (+.f64 alpha beta) (.f64 2 1)))

series1.4s

Counts

4 → 12

Calls

4 calls:

271.0ms	(+.f64 (+.f64 alpha beta) (*.f64 beta alpha))
438.0ms	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 3))
341.0ms	(/.f64 (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1) (+.f64 (+.f64 alpha beta) (.f64 2 1))) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 3)))
315.0ms	(/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1) (+.f64 (+.f64 alpha beta) (.f64 2 1)))

Iterations

Useful iterations: 0 (96.0ms)

Iter	Nodes	Cost
0	466	591
1	466	591
0	10	9
1	10	9
0	466	591
1	466	591
0	10	9
1	10	9
0	17	36
1	17	36
0	694	1347
1	694	1347
0	91	531
1	91	531
0	694	1347
1	694	1347
0	91	531
1	91	531
0	30	12
1	30	12
0	291	303
1	291	303
0	11	9
1	11	9
0	291	303
1	291	303
0	11	9
1	11	9
0	5559	39
0	263	195
1	263	195
0	12	21
1	12	21
0	263	195
1	263	195
0	12	21
1	12	21
0	10	3
1	10	3

simplify178.0ms

Counts

160 → 160

Iterations

Useful iterations: 0 (122.0ms)

Iter	Nodes	Cost
0	4940	5281
1	4940	5281

prune180.0ms

Filtered

120 candidates to 160 candidates (-33.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	160	0	160
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	160	8	168

Merged error: 0.0b

Counts

168 → 8

regimes57.0ms

Accuracy

93.7% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 3.7b

bsearch31.0ms

Steps

Iters	Range		Point
9	1860525970603186.5	1.3760313739509478e+24	18400915820535212.0

simplify6.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	45	108
1	45	108

end0.0ms

sample768.0ms

Algorithm

intervals

Results

476.0ms	8000×	body	80	valid
137.0ms	8000×	pre	80	true

Details

analyze5.0ms

sample27.0ms

simplify533.0ms

prune5.0ms

localize14.0ms

rewrite109.0ms

series1.5s

simplify62.0ms

prune218.0ms

localize17.0ms

rewrite149.0ms

series1.4s

simplify294.0ms

prune965.0ms

localize20.0ms

rewrite91.0ms

series1.2s

simplify72.0ms

prune246.0ms

localize15.0ms

rewrite89.0ms

series1.4s

simplify178.0ms

prune180.0ms

regimes57.0ms

bsearch31.0ms

simplify6.0ms

end0.0ms

sample768.0ms

Profiling